A new derivation of the finite $N$ master loop equation for lattice Yang-Mills
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916116595474432 |
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| author | Shen, Hao Smith, Scott A. Zhu, Rongchan |
| author_facet | Shen, Hao Smith, Scott A. Zhu, Rongchan |
| contents | We give a new derivation of the finite $N$ master loop equation for lattice Yang-Mills theory with structure group $SO(N)$, $U(N)$ or $SU(N)$. The $SO(N)$ case was initially proved by Chatterjee in \cite{Cha}, and $SU(N)$ was analyzed in a follow-up work by Jafarov \cite{Jafar}. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itô's formula. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2202_00880 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new derivation of the finite $N$ master loop equation for lattice Yang-Mills Shen, Hao Smith, Scott A. Zhu, Rongchan Probability Mathematical Physics Analysis of PDEs We give a new derivation of the finite $N$ master loop equation for lattice Yang-Mills theory with structure group $SO(N)$, $U(N)$ or $SU(N)$. The $SO(N)$ case was initially proved by Chatterjee in \cite{Cha}, and $SU(N)$ was analyzed in a follow-up work by Jafarov \cite{Jafar}. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itô's formula. |
| title | A new derivation of the finite $N$ master loop equation for lattice Yang-Mills |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2202.00880 |